Photoinduced hole hopping through tryptophans in proteins

Significance

Electron (hole) hopping through tryptophan residues activates protein cofactors, participates in cellular photosignaling, and protects enzymes from oxidative degradation. The energetics of excited chromophores, together with their positions relative to proximal indoles, are evolution-optimized in natural photolyases and cryptochromes. Our theoretical analysis of photoinduced hole hopping through tryptophans in rhenium-modified blue copper proteins has shed light on the roles of electronic coupling and adiabaticity, as well as electrostatic-field fluctuations and solvation dynamics in driving charge transport rapidly over long distances. The take-home message is that attention should be paid to solvation of redox-active molecules in hopping chains in the design of bioinspired light-harvesting systems and functional photocatalysts.

Abstract

Hole hopping through tryptophan/tyrosine chains enables rapid unidirectional charge transport over long distances. We have elucidated structural and dynamical factors controlling hopping speed and efficiency in two modified azurin constructs that include a rhenium(I) sensitizer, Re(His)(CO)₃(dmp)⁺, and one or two tryptophans (W₁, W₂). Experimental kinetics investigations showed that the two closely spaced (3 to 4 Å) intervening tryptophans dramatically accelerated long-range electron transfer (ET) from Cu^I to the photoexcited sensitizer. In our theoretical work, we found that time-dependent density-functional theory (TDDFT) quantum mechanics/molecular mechanics/molecular dynamics (QM/MM/MD) trajectories of low-lying triplet excited states of Re^I(His)(CO)₃(dmp)⁺–W₁(–W₂) exhibited crossings between sensitizer-localized (*Re) and charge-separated [Re^I(His)(CO)₃(dmp^•–)/(W₁^•+ or W₂^•+)] (CS1 or CS2) states. Our analysis revealed that the distances, angles, and mutual orientations of ET-active cofactors fluctuate in a relatively narrow range in which the cofactors are strongly coupled, enabling adiabatic ET. Water-dominated electrostatic field fluctuations bring *Re and CS1 states to a crossing where *Re(CO)₃(dmp)⁺←W₁ ET occurs, and CS1 becomes the lowest triplet state. ET is promoted by solvation dynamics around *Re(CO)₃(dmp)⁺(W₁); and CS1 is stabilized by Re(dmp^•–)/W₁^•+ electron/hole interaction and enhanced W₁^•+ solvation. The second hop, W₁^•+←W₂, is facilitated by water fluctuations near the W₁/W₂ unit, taking place when the electrostatic potential at W₂ drops well below that at W₁^•+. Insufficient solvation and reorganization around W₂ make W₁^•+←W₂ ET endergonic, shifting the equilibrium toward W₁^•+ and decreasing the charge-separation yield. We suggest that multiscale TDDFT/MM/MD is a suitable technique to model the simultaneous evolution of photogenerated excited-state manifolds.

Electron (hole) transport along chains of tryptophan (W) and tyrosine (Y) residues in proteins (1, 2) plays an essential role in delivering reducing or oxidizing equivalents to active sites in enzymes [ribonucleotide reductase (3–7), photolyase (PL) (8–15), cytochrome c peroxidase (16–18), methylamine utilization protein MauG (19), laccases (20–22), and respiratory complex I (23)], signaling [cryptochromes (CRY)] (8, 13, 24), as well as in protecting oxidases from self-damage (20, 25–27) by transporting high-potential holes to the protein surface where they can be disarmed by cellular reductants. It also is likely that electron hopping through multiheme bacterial cytochromes is responsible for reduction of extracellular mineral acceptors (28–31) whereas chains of FeS clusters carry electrons, for example, in the respiratory complex I (32, 33) and hydrogenases (34). Nearly all these processes are thought to involve nonadiabatic electron-tunneling steps between W, Y, heme, or FeS-cluster sites.

To investigate the factors controlling multistep electron tunneling (hole hopping), we covalently attached an Re^I(CO)₃(dmp)⁺ photooxidant (abbreviated Re) (4,7-dimethyl-1,10-phenanthroline [dmp]) to surface histidines H124 or H126 in the blue copper protein Pseudomonas aeruginosa azurin and engineered an artificial hopping pathway by inserting one or two tryptophan residues between the Re and Cu^I sites, affording mutants ReH124W122 (Re124W) (35) and ReH126W124W122 (Re126WW) (36). Near- ultraviolet (UV) excitation of the appended Re complex triggered hole hopping through tryptophan(s), ultimately oxidizing the Cu^I site (35–39) (Scheme 1). While similar in operation to natural photoenzymes, such as PLs and CRYs, Re124W or Re126WW show important quantitative differences whose understanding will help designing protein-based photocatalysts, solar-energy harvesting systems, and bioelectronic devices.

Scheme 1.

Phototriggered electron transport in Re124W (35, 37) and Re126WW (36, 38) Cu^I azurins. Optical excitation of the ground-state (GS) Re complex to the metal to ligand charge transfer (¹MLCT) state is followed (39, 40) by ∼150-fs intersystem crossing to hot triplet state(s) ^#*Re that undergo picosecond relaxation to the lowest triplet state *Re of mixed charge transfer (Re(CO)₃→dmp)/intraligand (ππ*-dmp) character (CT/IL). ET from the proximal tryptophan results in the charge-separated state (CS1) Re^I(CO)₃(dmp^•−)(H124)(W122^•+)Cu^I or Re^I(CO)₃(dmp^•−)(H126)(W124^•+)(W122)Cu^I. In Re124W azurins, Cu^I→W122^•+ ET in CS1 produces the redox product (RP) Re^I(CO)₃(dmp^•−)H124W122Cu^II. The cycle is then closed by ∼3-μs dmp^•–→Cu^II back ET. In Re126WW, the CS1 state is converted to CS2 by W124^•+←W122 ET (the second hole “hop”). RP formation and ∼120-μs back ET follow. Electron transport occurs over 19 (Re124W) and 23 Å (Re126WW).

Importantly, electron transport from Cu^I to the electronically excited Re complex (*Re) is 300× (Re124W) and 10,000× (Re126WW) faster than estimated for single-step hole tunneling over the same distances although the much greater accelerating effect of two tryptophans comes at the expense of a lower yield (36). Such a lower yield is not observed for PLs or CRYs where charge separation between the flavin chromophore and the surface tryptophan (or tyrosine) occurs through two or three intervening tryptophans with a quantum yield of about 0.2 (12). We would like to know whether different protein and tryptophan solvation dynamics are responsible for the lower charge-separation efficiency in Re126WW compared to evolution-optimized natural photoenzymes. In addition, while electron transfer (ET) from the proximal tryptophan to the photoexcited chromophore in all these systems (and in flavodoxins) (41, 42) is influenced by electronic coupling between aromatic rings, the ET time constants depend on the nature of the chromophore, ranging from 0.4 to 0.8 ps (CRYs) (10, 24) or 30 to 45 ps (PLs) (11, 12) to ∼500 ps in Re-azurins.

Here, we present results of a theoretical study designed to shed light on the roles of solvent/protein fluctuations that control hole hopping in Re124W and Re126WW. To this end, we have developed a multiscale quantum mechanics/molecular mechanics/molecular dynamics (QM/MM/MD) procedure to calculate the temporal evolution of a manifold of low-lying excited states of the active cofactors by time-dependent density-functional theory (TDDFT) while protein and water dynamics are simulated classically (Fig. 1). In simulations performed on reactive *Re states, we searched for conditions that would convert the systems to the charge-separated state CS1.

Fig. 1.

Parts of Re124W (Left) and Re126WW (Right) azurins treated by quantum (QM, stick representation) and molecular (MM, cartoon representation of the protein secondary structure) mechanics. The QM regions consisted of Re(CO)₃(dmp)H124G123W122 and Re(CO)₃(dmp)H126L125W124G123W122 azurin fragments, respectively. The MM parts also included water molecules and the Cu^I atom.

Results and Discussion

Approach.

We have modeled the conversion between the lowest triplet excited state (*Re) and the lowest CS1 state in Re124W and Re126WW. This conversion corresponds to the excited-state ET process responsible for ∼90% of the photoinduced charge separation between the Re complex and the proximal tryptophan, W122 or W124, respectively (35–37). Aiming at a qualitative understanding of ET-promoted structural and solvational dynamics, we have employed a multiscale QM/MM/MD procedure that describes the system in full, including explicit water and the protein environment (Fig. 1) and treating the active part at a TDDFT level with the Perdew–Burke–Ernzerhof hybrid functional (PBE0) appropriate for systems containing a heavy-metal atom. To make these simulations computationally feasible, we performed Born–Oppenheimer (BO) dynamics. Although we calculated several low-lying triplet excited states simultaneously, population of higher states around the crossing region was prevented by neglecting the time evolution of the total electronic wave function together with the absence of nonadiabatic couplings (43). Approximating the ET step by a two-state model (44, 45), we searched for conditions leading to the change of the character of the lowest triplet state from *Re to CS1. Calculations consisted of three steps: 1) MM/MD simulations of solution structures of both Re-azurins in their ground state (SI Appendix, Fig. S1) and lowest triplet excited state (*Re) (Fig. 2 and SI Appendix, Fig. S3), using unique sets of realistic MM parameters for the ground state and excited state of Re(imidazole)(CO)₃(dmp)⁺ in the protein environment (derived in SI Appendix, section S13 and spectroscopically validated in SI Appendix, Fig. S2). Classical MM/MD excited-state trajectories, which modeled the “slow” evolution of the reacting system due to protein and solvent motion, provided a set of starting geometries and velocities for subsequent QM/MM/MD. 2) In the next step, we ran unrestricted Kohn–Sham (UKS) QM/MM/MD simulations of the lowest triplet state, starting from six different points at MM trajectories of each *Re124W and *Re126WW, denoted by capital letters in Fig. 2, Top. UKS/MM/MD trajectories characterized the reactive state *Re (Fig. 2 and SI Appendix, Figs. S5 and S6) and adjusted the structure and solvation to the actual *Re charge distribution. 3) From each of the UKS trajectories, we chose two or three snapshots serving as starting points for TDDFT QM/MM/MD trajectories that mapped the temporal evolution of a set of low-lying electronic states (Figs. 3 and 4; all calculated trajectories are in SI Appendix, Figs. S7 and S8).

Fig. 2.

Time evolution of the *Re state of Re124W and Re126WW. (Top) Classical MM trajectories of closest Re-indole (Re-C) and dmp-indole (C-C) distances calculated with *Re parametrization. Black vertical lines denote starting times for UKS dynamics. (Middle and Bottom) Typical UKS/MM/MD spin and charge trajectories of the lowest triplet excited state (*Re) showing fluctuations between the ³CT and ³IL character. Limiting ππ*(dmp) ³IL is described by spin 0 at Re and 2 at dmp, limiting the CT character by spin 1 at both dmp and Re(CO)₃. Numbered vertical lines denote starting times for TDDFT/MM/MD simulations. Spin-density distributions in typical ³CT/³IL and ³IL structures are displayed in SI Appendix, Fig. S4 and all calculated UKS trajectories in SI Appendix, Figs. S5 and S6.

Fig. 3.

TDDFT energy trajectories of the six lowest triplet excited states of Re124W (L-1) and Re126WW (A-3) in the proximity of *Re/CS1 crossing. (Behavior over a longer 0.3-ps interval is shown in SI Appendix, Fig. S9.) Blue, Re(imidazole)(CO)₃(dmp)⁺-localized *Re-type states defined by >0.5 total charge on the Re complex; red, states with predominant CS1 character defined by >0.5 total charge on the proximal indole; green, states with predominant CS2 character defined by >0.5 total charge on the W122 indole in Re126WW. Arrows and dotted vertical lines denote the calculated crossing times.

Fig. 4.

Typical TDDFT/MM/MD charge trajectories of the lowest triplet excited state and *Re-CS1 electronic coupling. Changes in the charge distribution between Re(CO)₃ and dmp manifest changing *Re electronic structure caused by varying ³IL and ³CT contributions. Vertical jumps signify *Re/CS1 crossings (i.e., *Re(CO)₃(dmp)⁺←W ET), after which the charge distribution stabilizes in the CS1 state. B-3 exhibits also a CS1/CS2 crossing (W124^•+←W122 second “hop”). Black histograms show electronic couplings between the lowest *Re and the lowest CS1 states up to their crossing; the last bar occurs approximately at the time corresponding to ∼1/2 of the charge jump. All calculated trajectories and couplings are displayed in SI Appendix, Figs. S7, S8, S13, and S14.

For Re124W, we have calculated 12 TDDFT/MM/MD trajectories that all exhibited an *Re/CS1 state crossing. Out of the 17 calculated Re126WW trajectories, 9 showed *Re/CS1 crossings, 1 started in CS1, and 7 trajectories indicated an *Re/CS2 crossing. One trajectory (B-3) exhibited both *Re/CS1 and CS1/CS2 crossings, fortuitously providing insight into the second hop: i.e., W124^•+←W122 ET. TDDFT trajectories were then analyzed in terms of electronic coupling between the *Re and CS1 states and accompanying structural/solvational changes. Emerging common patterns helped to unravel conditions promoting ET, even in the absence of statistical evaluation, which was not possible, owing to computational-time demands of TDDFT/MM/MD.

Reactive Excited State (*Re).

The W122 indole and the dmp ligand in *Re124W occur in two nearly stacked orientations, with average angles between their planes of ∼20° and 34°. In each conformation, they slightly fluctuate around their mean positions and an average closest C–C distance of 3.2 Å (Fig. 2, Top and SI Appendix, Fig. S3). In *Re126WW, the W124 indole and dmp are mainly T-oriented (73 ± 12°), with an average shortest distance of 3.45 Å. Rotations of Re(CO)₃(dmp)⁺ around the Re–N(His126) bond at 27 and 31 ns reversibly switch the system to a short-lived conformation, with dmp pointing away from the W124 indole, in which it spends 6% of the MD simulation time.

In agreement with previous work on ReL(CO)₃(polypyridyl) complexes (40, 46–51), UKS/MM/MD trajectories showed that *Re arises from a combination of dπ(Re(CO)₃)→π*(dmp) ³CT and π→π*(dmp) ³IL (intraligand) excitations, roughly described as Re^II(His)(CO)₃(dmp^•–)⁺ and Re^I(His)(CO)₃(*dmp)⁺, respectively. Relative contributions of the ³CT and ³IL components fluctuate with time, making the *Re electronic structure time dependent. In particular, the excited electron stays in the π*(dmp) orbital while hole (de)localization varies in time between dmp (³IL) and Re(CO)₃ (³CT).

This behavior was demonstrated by anticorrelated variations of Mulliken charge and spin (difference of α-, β-spin electron populations) on dmp and Re(CO)₃ along UKS/MM/MD trajectories (Fig. 2 and SI Appendix, Figs. S4–S6). In particular, the spin at dmp varies between 2 (for ³IL) and ∼1.2 [corresponding to the predominant ³CT character with a minor ³IL contribution (³CT/³IL)]; and the spin at Re(CO)₃ varies between 0 and ∼0.8. Charges vary simultaneously from about +0.4 at both Re(CO)₃ and dmp for ³IL to ∼+0.8 and –0.15, respectively, for ³CT/³IL. Interestingly, some spin and charge delocalization to W122 is seen in ³IL sections of most Re124W trajectories. All these features are displayed by trajectory L that switches from ³CT/IL to mainly ³IL around 1.5 ps (Fig. 2).

*Re/CS1 Crossing.

The time evolution of a manifold of low-lying triplet excited states was monitored by TDDFT/MM/MD; these states were characterized as *Re, CS1, or CS2 by Mulliken charges at the Re complex and the corresponding tryptophan indole(s). Individual trajectories differed by the starting snapshot taken from previously calculated UKS/MM/MD trajectories. Typical energy trajectories (Fig. 3) revealed the presence of several *Re-type states followed in energy by one or more CS1-type states. With time, CS1 state(s) underwent multiple crossings with other higher lying states, while decreasing in energy, and then occasionally approached and finally crossed the trajectory of the lowest *Re state, becoming the lowest triplet state.

The *Re/CS1 crossing [i.e., the *Re(His)(CO)₃(dmp)⁺←W ET event] was clearly manifested on TDDFT/MM/MD trajectories following the charge distribution in the lowest triplet excited state (Fig. 4 and SI Appendix, Figs. S7, S8, and S10), which showed a unit rise of the Mulliken charge at the indole and a concomitant drop at Re(CO)₃(dmp), in line with the Re^I(H124)(dmp^•–)(W122^•+) or Re^I(H126)(dmp^•–)(W124^•+)(W122) formulation of the CS1 state. The charge decrease on Re(CO)₃(dmp) was mostly localized at dmp if the switchover occurred from an *Re state of the predominantly IL character (typically K-1, K-2, M-2, N-1, N-2, B-2, C-2, and C-3) or delocalized over both Re(CO)₃ and dmp if there was a substantial CT character in *Re (L-1, M-1, O-1, O-2, P-1, P-2, A-1, A-3, B-3, and D-1). Interestingly, including the 20 nearest water molecules into the QM space caused the A-1 *Re/CS1 crossing to take place ∼20 fs earlier. Charges at individual water molecules fluctuated randomly in a narrow range, and changes of charges at O-atoms indicated only small electronic polarization of the H₂O molecules closest to the indole N-H groups in response to the *Re→CS1 conversion (SI Appendix, Fig. S10).

After the crossing, both proteins were stable in their CS1 states, in agreement with the finding (35) that *Re←W ET is slightly exergonic (∼30 meV; K ≅ 3 for Re124W), and the second “hop” producing CS2 in Re126WW is slower (36). *Re/CS1 crossings and a stable CS1 were detected also on trajectories obtained with different computational protocols and/or using the CAM-B3LYP functional (SI Appendix, section S6).

Calculated *Re/CS1 crossing times varied between trajectories, but they all fell within the first 2.5 ps. Experimentally, *Re←W ET is a multiphase process whose kinetics were fitted with ∼300- and 500-ps time constants attributed to reactions from hot and (nearly) relaxed *Re, respectively (Scheme 1) (35). The difference between calculated crossing and experimental ET times is caused by TDDFT/MM/MD simulations starting in configurations close to the transition state. The simulated system contained some extra energy released upon the transition from MM to UKS and then from UKS to TDDFT, some of which could have been deposited in ET-enabling modes, above the *Re energy minimum. Given the low height of the reaction barrier (0.19 eV, estimated from Marcus theory), it is highly probable that TDDFT/MM/MD starting points were placed close to the top of the barrier and the trajectories monitored mostly fast ET-driving modes. This argument can be recast in the spirit of the Sumi–Marcus model (52, 53), whereby slow system evolution (solvent, protein) is modeled classically (MM/MD), while reaction along the “fast” coordinate (some fast solvent motions, intracofactor vibrations) (SI Appendix, section S12) is sampled by TDDFT/MM/MD trajectories starting from randomly chosen points on the “slow” coordinate.

Electronic Coupling.

Avoided crossing between the lowest *Re and CS1 states on TDDFT trajectories demonstrated that dynamical fluctuations of solvated *Re-azurins create situations where oxidation of the proximal tryptophan by an electronically excited Re complex is energetically feasible, leading to a localized CS1 state. Calculating electronic coupling H_ab between *Re and CS1 diabatic states in the crossing region enabled us to assess whether the studied ET approaches the adiabatic or nonadiabatic limit (45, 53–55) and, thus, whether a strong ET rate dependence on |H_ab| should be expected. We employed the fragment charge differences (FCD) form of the generalized Mulliken–Hush (GMH) method (56–58) to estimate transformation to the diabatic representation revealing strong coupling for most trajectories (Fig. 4 and SI Appendix, Figs. S13 and S14), with root-mean-square (rms) values of 60 (Re124W) and 20 meV (Re126WW) at the tops of activation barriers (crossing points in the diabatic representation), with a large spread between trajectories: 13.2 to 97.0 and 0.1 to 41.7 meV, respectively; the more strongly coupled ones occurred more frequently (SI Appendix, Tables S1 and S2); and even larger values were occasionally calculated at earlier times before crossings.

Coupling variations between and along trajectories result from a combination of electronic and steric effects. Larger |H_ab| values calculated for Re124W than Re126WW reflect different indole/dmp relative positions: stacked (parallel-displaced, [PD]) and T-oriented, respectively. For each species, coupling was larger when *Re had more ³IL character (K-1, K-2, and M-2) as compared to ³CT/³IL (O-1, O-2, and P-2). A similar trend was seen for Re126WW, where strongly coupled B-2 and C-2 had an essentially ³IL character before the crossing, whereas the only two weakly coupled cases, B-1 and D-3, exhibited large charge fluctuations toward ³CT in the crossing region. In some cases, both the IL contribution to the reacting *Re state and H_ab increased as the trajectory approached the crossing (L-1, P-1, A-1). Pronounced fluctuations increasing the ³CT character on C-3 at ∼0.31 and 0.615 to 0.665 ps were accompanied by markedly lower H_ab values, compared to the rest of the trajectory, where *Re was predominantly ³IL. Changes in the excited-state character alone cannot explain all coupling variations and must be considered together with geometric factors: namely, the indole–dmp distance, as well as the angle between the aromatic planes (SI Appendix, Tables S1 and S2 and Figs. S15 and S16, and discussion in SI Appendix, section S8). In general, strong coupling in Re124W was favored by a 20° to 30° tilt and by the indole benzene ring lying above dmp C5–C6 or C3–C4 bonds (central and side rings, respectively) (SI Appendix, Fig. S15). The dependence on the closest distance was rather weak, observable only for trajectories with the same *Re character (e.g., M-2, N-2, N-1). In Re126WW, strong coupling occurred in cases where the indole was positioned sideways and nearly parallel to the C7–C8 bond of the dmp side ring (SI Appendix, Fig. S16), and the angle between the two aromatic planes deviated from an ideal 90° T-configuration to ∼75°. The coupling dependence on the dmp/indole geometry, as well as on the *Re electronic structure, likely reflects changes in the frontier-orbital overlap involved in ET (indole highest occupied molecular orbital [HOMO], dmp-localized lowest unoccupied molecular orbital [LUMO], LUMO+1, and low-lying π orbitals that are depopulated upon ³IL excitation) (SI Appendix, Figs. S17 and S18).

Adiabaticity.

Although average H_ab values predict *Re(CO)₃(dmp)⁺←W ET in *Re126WW to be ∼10× slower than in *Re124W, comparable rates (∼500 ps)^–1 were determined experimentally for both species (Scheme 1) (35–38), as well as for similar interfacial ET in Re126T124W122 (59). These observations, together with the relatively large |H_ab| values, suggest that ET is adiabatic, largely controlled by the effective frequency of nuclear motion along the reaction coordinate, ν_eff. Indeed, using the average coupling values and a typical (2, 35) reorganization energy λ = 0.8 eV, *Re(CO)₃(dmp)⁺←W ET does not meet the nonadiabaticity condition requiring the Landau–Zener parameter 2πγ = π^3/2<H_ab²>/hν_eff√(λk_BT) to be << 1 (45, 60), unless ν_eff is unrealistically large (2πγ of 0.1 would require ν_eff = 3.4 × 10¹⁴ s^–1 [11,360 cm^–1] for Re124W or 3.8 × 10¹³ s^–1 [1,260 cm^–1] for Re126WW). The same conclusion can be reached in a medium-fluctuation controlled regime (54, 55) where the adiabaticity contribution is estimated using a parameter κ = 4πH_ab²<τ>/ħλ where <τ> is the medium relaxation time induced by a constant charge distribution (54, 55, 61). Setting κ ≥ 1 as a limit for an adiabatic reaction would require <τ> ≥ 12 fs for *Re124W and ≥ 100 fs for *Re126WW, using rms H_ab values of 60 and 20 meV, respectively. Relaxation times indicated by electrostatic-potential trajectories (200 to 600 fs, discussed in Electrostatic Potential) and time-resolved spectroscopic experiments (pico/nanoseconds) (48, 62), lie well above these limits, supporting the conclusion of *Re(CO)₃(dmp)⁺←W ET adiabaticity. (We note that these adiabaticity arguments are valid over a broad range of λ values, approximately for λ < 2.5 eV. In addition, trajectories with above-average |H_ab| values can be expected to dominate the process, further lowering the upper limits of relaxation times.)

Water Distribution.

Solvation of the W122-indole in *Re124W and W124-indole (*Re126WW) strengthened along TDDFT/MM/MD trajectories as the system approached the *Re/CS1 crossing region, becoming CS1-like shortly before the actual crossing. This behavior indicated that water fluctuations around indole facilitate *Re(CO)₃(dmp)⁺←W ET by driving the system in the direction of the CS1 product.

We have quantified solvation by a water proximal radial distribution function g(r) (63, 64) calculated around the indole(s) and averaged over relevant parts of trajectories showing an *Re/CS1 crossing (SI Appendix, Fig. S19). The g(r) around W122 in *Re124W or W124 in *Re126WW peaked below 2.0 Å due to water molecule(s) H-bonded to the indole N–H group, followed by a broad maximum (second solvation layer) at 2.5 to 3.2 Å (Fig. 5). The g(r) calculated over a 20-fs interval before the *Re/CS1 crossing was either shifted closer to the indole (W122 in *Re124W), or the first peak sharpened and increased in intensity (W124 in *Re126WW), resembling in each case g(r) averaged over CS1 regions after the crossing. In the both cases, the ratio of g(r) magnitudes at the first maximum and the following minimum was higher during 20 fs before the crossing and in the CS1 region compared to the *Re average, indicating (65, 66) that solvating water molecules become more strongly H-bonded to the indole and partly disconnected from the second solvation layer just before the crossing (this situation continues in the CS1 product). Gradual “tightening” of indole solvation on approach to the *Re/CS1 crossing also is manifested by g(r) calculated over subsequent 100-fs intervals along averaged trajectories, as well as the single A-1 trajectory (SI Appendix, Fig. S20). Solvation of the distal W122 indole in *Re126WW also strengthens upon *Re/CS1 conversion (Fig. 5, Bottom), suggesting that emergence of the positive charge at W124 attracts water molecules to the entire W124⋅⋅⋅W122 region. However, the W122 indole was always solvated less and more weakly H-bonded than W124, as documented by the first g(r) maximum occurring ∼0.1 Å farther and by a smaller max/min ratio. Space-filling models (Fig. 5) revealed that W122 is much less water-exposed than W124, being partly shielded by a L120A119S118 α-helix whose A119 backbone oxygen atom occasionally becomes H-bonded to the NH group (SI Appendix, Figs. S21 and S22).

Fig. 5.

(Left) Water proximal radial distribution function g(r) around W122 indole in Re124W (Top Left), W124 in Re126WW (Middle Left), and W122 in Re126WW (Bottom Left) averaged over full-length TDDFT trajectories before (red) and after (blue) the *Re/CS1 crossing; dashed-dotted curves are the corresponding integrals. Green dotted curves, g(r) averaged over 20 fs before *Re/CS1 crossing. (Top Right) A space-filling model of *Re124W shows Re(CO)₃(dmp)⁺ and the W122 indole half-buried in the protein and indole NH in close contact with O(A119), indicated by the yellow arrow. The indole plane faces dmp from one side. (Bottom Right) In *Re126WW, the dmp ligand is water-exposed, and W124-indole protrudes into the solvent (green arrow). W122 indole NH is in a close contact with O(A119). Snapshots taken from *Re MM trajectories (Fig. 2, Top) at 11,500 and 24,600 ps, respectively.

Electrostatic Potential.

Environmental effects were monitored in real time by calculating the electrostatic potential at the indoles [φ(W)] and the Re(imidazole)(CO)₃(dmp) complex [φ(Re)] generated by all water molecules (φ_H2O), the whole classical part (protein plus water, φ_MM), or the full system including the rest of the QM region (φ_tot, defined in SI Appendix, Fig. S23 and section S13.4). We found that decreasing the negative potential at the proximal indole and increasing the potential at the Re complex facilitated system evolution toward the *Re/CS1 crossing. This behavior is attributable to electrostatic stabilization of the positive indole and negative dmp charges in CS1, in combination with *Re destabilization when φ(Re) at the positively charged Re complex increased. The φ-variations appeared to be mainly a collective effect arising from a solvation shell shared between the Re complex and the close-lying indole. Upon crossing, CS1 was instantaneously stabilized electrostatically by short-range electron-hole interactions between Re^I(dmp^•–) and indole^•+. Solvent restructuring and polarization contributed less and took up to 600 fs to develop.

The differences between the potentials at the Re complex and the proximal indole Δφ_x = φ_x(Re) – φ_x(W) (x = tot or H₂O) and between the CS1 and *Re energies ΔE along individual trajectories are anticorrelated: Compare red and black curves in the left column of Fig. 6 and the histogram of correlation coefficients below. Large negative correlation coefficients (–0.7 [Δφ_tot] and –0.6 [Δφ_H2O], averaged over all trajectories) were observed when calculated over full trajectory lengths (Fig. 6), as well as during the last 100 fs before *Re/CS1 crossing (–0.7 for both Δφ_H2O, Δφ_tot) (SI Appendix, Fig. S26). The highest values were often obtained when the ΔE trajectory was shifted by 1 to 6 fs behind the Δφ_tot trajectory (i.e., φ_tot drives, ΔE follows). Correlating φ_tot(W) instead of Δφ_tot gave a lower coefficient of 0.5. The Δφ_tot temporal evolution largely copied Δφ_H2O, whose fluctuations were slightly broader and encompassed more frequent finer Δφ_tot oscillations (originating in fast intramolecular modes) (SI Appendix, section S12). Importantly, φ_H2O(W) and φ_H2O(Re) separately correlated with ΔE less, with lower coefficients of 0.3 and –0.4, respectively. The better ΔE correlation with Δφ_H2O than with φ_H2O(W) or φ_H2O(Re) individually implies a collective effect of fluctuating solvation around *Re⋅⋅⋅W moieties.

Fig. 6.

(Left Column) Time evolution of the CS1–*Re energy difference ΔE (black, left axis), potential difference Δφ = φ(Re) – φ(W) (W, proximal indole, Δφ_tot in red, Δφ_H2O in green), and φ_tot(W) (blue) calculated along typical trajectories O-1 (Re124W) and D-1 (Re126WW) up to the *Re/CS1 crossing. (Right) Trajectories of φ_tot (red, blue) and φ_H2O (black, green) at the Re complex and the proximal indole before and after *Re/CS1 crossing (marked by vertical dotted lines). (Bottom Histogram) Correlation coefficients between time evolutions of ΔE and Δφ_tot, φ_tot(Re), φ_tot(W), Δφ_H2O, φ_H2O(Re), and φ_H2O(W) calculated over individual TDDFT trajectories up to the *Re/CS1 crossing. Positive and negative values are for correlation and anticorrelation, respectively. More trajectories, φ at individual fragments, and correlation coefficient diagrams are shown in SI Appendix, Figs. S24–S29.

*Re/CS1 crossing was accompanied by a virtually instantaneous rise of φ_tot(Re) and nearly coincidental φ_tot(dmp), and a concomitant drop of φ_tot(W), owing to the emergence of a Re(dmp^•–)⋅⋅⋅W^•+ interaction (right columns of Fig. 6 and SI Appendix, Fig. S24). On the other hand, φ_H2O(W), φ_H2O(Re), and nearly parallel φ_H2O(CO) did not exhibit abrupt changes. Instead, they slowly decreased and increased, respectively, during 200 to 600 fs after the crossing, owing to solvent readjustment to the new charge distribution. The φ_H2O(W122) in Re126WW also decreased during ∼600 fs after *Re/CS1 crossing (SI Appendix, Fig. S29), due to higher water abundance in its vicinity, which also was indicated by a higher g(r) (Fig. 5, Bottom Left). However, φ_tot(W122) slightly increased, owing to a positive charge at the neighboring W124^•+.

Notably, all φ_MM trajectories were nearly parallel with φ_H2O ones, only shifted lower because of a negative, virtually constant potential generated by protein atoms (SI Appendix, Fig. S28). Apparently, protein reorganization does not contribute on the short timescales of TDDFT trajectories.

The Second Hop in Re126WW.

This hop was observed only along the B-3 trajectory (Fig. 4). Whereas strong coupling at three snapshots in the CS1/CS2 crossing region (17, 35, and 58 meV) favors fast and possibly adiabatic W124^•+←W122 ET, electrostatic-potential trajectories indicate that gradual water restructuring around W122 in CS1 in the direction of the CS2 product is needed to drive the CS1→CS2 conversion (a rare event exhibited by only one trajectory). Also, the experimentally established (36) CS1→CS2 endergonicity was attributed to weaker W122 (than W124) solvation and weaker coulombic interaction of Re(dmp^•–) with W122^•+ in CS2 than with W124^•+ in CS1.

The W122-indole in Re126WW is much less exposed to water than W124 (Fig. 5). In CS1, the first W122 g(r) maximum and the corresponding integral are nearly 7× and 2.3× lower for W122 than W124^•+ (Fig. 5). W122 solvation increases upon its oxidation to W122^•+ in CS2, owing to a water shift from the second solvation sphere and the W124 vicinity, but it remains low compared to W124, as well as to W124^•+ in CS1 (SI Appendix, Fig. S30). (In the CS1/CS2 region, the W122^•+ NH group interacts directly with a single H₂O molecule and the A119 oxygen [SI Appendix, Fig. S22].)

The φ_H2O(W122) gradually decreases as the system evolves across the B-3 CS1 region, presumably due to water restructuring. Although this decrease amounts only to ∼0.33 V, it could decrease the CS2 energy, allowing the system to reach the CS1/CS2 crossing point. The φ_H2O(W122) decreases by another ∼1 V over a ∼250-fs period after the crossing as the solvation responds to W122^•+ formation, stabilizing the CS2-product. On the contrary, coulombic forces in the QM region result in destabilization of the CS2 product since Re(dmp^•–)⋅⋅⋅W124^•+ in CS1 is replaced by a weaker Re(dmp^•–)⋅⋅⋅W122^•+ interaction, which is manifested by a decrease of φ_tot(Re) and φ_tot(dmp) at CS1/CS2 crossing (SI Appendix, Fig. S31, Right).

*Re/CS2 Crossing.

Several TDDFT trajectories indicated the possibility of a direct *Re(CO)₃(dmp)⁺←W122 ET in Re126WW, bypassing the W124^•+ intermediate. Analysis of typical trajectories A-2 and C-1 suggested that *Re/CS2 crossing is favored by a fortuitous water arrangement around both W122 and W124 indoles. The difference between φ_tot at W124 and W122 increases in the course of ∼200-fs (A-2) and 40-fs (C-1) intervals before the crossing, almost entirely due to changes in φ_H2O. At the *Re/CS2 crossing, φ_tot(W122) becomes lower than φ_tot(W124) by 0.6 to 0.8 V while g(r) indicates a small shift of solvating water from W124 to the W122 indole on going from *Re to CS2 (SI Appendix, Figs. S32 and S33). Although *Re→CS2 conversion occurs along several trajectories, it is uncompetitive with sequential hopping because of weak *Re−CS2 electronic coupling (≤0.3 meV). This drawback could, in principle, be overcome by flickering resonance whereby *Re, CS1, and CS2 states would be temporarily isoenergetic, enabling ballistic ET (67, 68). Alas, we did not find resonant behavior on A-2 or C-1 energy trajectories before the *Re/CS2 crossing. Instead, CS2 became the lowest triplet state through a rapid series of avoided crossings with CS1 and *Re states (SI Appendix, Fig. S34).

Concluding Remarks

In agreement with the experimentally established reaction mechanism (Scheme 1), our simulations accord with sequential electron transfer between localized redox sites in Re126WW. Importantly, our work suggests ET adiabaticity, indicating that reactive states are driven toward crossings by collective solvent fluctuations around *Re(CO)₃(dmp)⋅⋅⋅W and W124⋅⋅⋅W122 moieties while solvation and coulombic interactions between the Re complex and the indole(s) are major contributors to ET energetics.

The first ET step [*Re(CO)₃(dmp)⁺←W] is facilitated by fluctuations of the *Re excited-state electronic structure from predominantly Re(CO)₃→dmp ³CT to ππ*(dmp) ³IL. Whereas the excited electron stays localized on the dmp ligand, the hole fluctuates from Re(CO)₃ to dmp. *Re/CS1 crossings feature stronger electronic coupling when *Re acquires a predominantly ³IL rather than mixed ³CT/³IL character. This behavior is qualitatively rationalized in Fig. 7, showing that ³IL matches the through-space dmp⋅⋅⋅indole pathway where ET is facilitated by a shorter effective distance than in a ³CT-type *Re state. Moreover, ET to a predominantly ³CT state would require weakly coupled electron tunneling through a negatively charged dmp ligand or a Re^II←dmp^•–←indole charge shift (formally a simultaneous double-ET). Indeed, trajectories with a high ³CT contribution at the *Re/CS1 crossing (P-2, B-1, and D-3) exhibited the smallest |H_ab| values (SI Appendix, Tables S1 and S2). Similar arguments apply to guanine oxidation in DNA with intercalated ³IL-excited Re(pyridine)(CO)₃(dppz)⁺ (70) and, more generally, to any system where an electron donor interacts directly with a polypyridyl ligand of an electronically excited d⁶-metal complex.

Fig. 7.

W122→*Re(H124)(CO)₃(dmp)⁺ ET in ³IL (Left) and ³CT (Right) states. (Top) MO diagrams. (Bottom) Hole localization in predominantly ³IL (Left) and mixed ³CT/³IL (Right) *Re states, calculated as *Re electron detachment densities (69) on snapshots N-1, 1 ps and L-1, 0.25 ps, respectively.

*Re–CS1 and CS1–CS2 electronic couplings are substantial, making Re(CO)₃(dmp)⁺←W ET (also W124^•+←W122 ET in Re126WW) adiabatic, driven by solvation dynamics that bring *Re and CS1 (or CS1 and CS2) states to energetic degeneracy at the crossing points. Considering that comparable coupling values were calculated for interactions between various aromatics and their radical anions or cations (71, 72), as well as between some of the tryptophan and tyrosine residues in enzyme protective pathways (73), it is possible that the more efficient natural redox enzymes combine short-range adiabatic ET steps with nonadiabatic tunneling at longer distances as an additional means of control, depending on coupling magnitudes and environmental dynamics. [Interestingly, electrochemical reduction of cytochrome c attached to gold electrodes by linkers of variable lengths exhibited a switchover from nonadiabatic to a solvent/protein friction-controlled (adiabatic) mechanism at short distances (74, 75).]

Differences in Re124W/Re126WW and PL/CRY kinetics are qualitatively attributable to different reaction barriers as would be expected for adiabatic reactions. Optical excitation of a flavin quinone (flavin-adenine dinucleotide [FAD]) or semiquinone (FAD^•–) in PL/CRY triggers sequential ET along a conserved tryptophan triad, producing long-range charge separation on a picosecond timescale (10–12, 14, 15, 24). Both flavin ππ* and *Re(CO)₃(dmp)⁺ excited states are electronically coupled with proximal tryptophan indoles by through-space π-interactions between aromatic rings. An average |H_ab| of ∼7 meV (fluctuating up to 80 meV) was estimated computationally for a plant CRY (76) and 14 to 15 meV experimentally for a similar flavodoxin (41). Charge separation between the excited chromophore and proximal tryptophan is faster in PL/CRY [0.4 to 0.8 ps (*FAD) (10, 24) or 30 to 45 ps (*FAD^•−) (11, 12)] than in Re124W/Re126WW (∼500 ps) (Scheme 1). This difference is attributable to larger driving forces (–ΔG^o) in PL/CRY [–0.7 (*FAD) (10) and –0.4 eV (*FAD^•−) (12)] vs. –0.03 eV in Re124W (35) that translate to 1,300× and 210× larger Franck–Condon factors for *FAD and *FAD^•– redox centers in PL/CRY than in Re124W/Re126WW (assuming λ = 0.8 eV). Correcting experimental ET rates for different barrier heights leads to comparable preexponential terms for *chromophore←W₁ ET in PL/CRY and Re-azurin systems, supporting the proposed adiabaticity. Hole hopping between indoles in PL/CRY tryptophan triads is a picosecond process where the first (W₁^•+←W₂) and second (W₂^•+←W₃) ET steps occur in ≤9 and 30 to 50 ps, respectively (11, 12, 15, 24); these ET reactions are facilitated in the highly unequilibrated W₂^•+ solvent environment, which decreases the effective reorganization energy (15, 24, 77, 78). The latter effect is missing in Re126WW where W124^•+←W122 ET (<3 ns) is energetically uphill and W124^•+ is relatively long-lived.

Comparing Re124W/Re126WW with PL/CRY highlights the importance of solvation and water fluctuations in determining the energetics and dynamics of hopping processes. The chromophore and proximal tryptophan (W₁) are inside the protein core, largely shielded from solvating water, while the second and third tryptophans are progressively more water-exposed. Increasing solvation stabilizes W⁺ compared to neutral W, creating a redox-potential gradient that drives the positive charge (hole) along the hopping pathway from the protein interior toward the surface in a series of exergonic ET steps (12, 77–80). Such an energy gradient is missing in Re126WW where hopping proceeds at a water-exposed protein surface, and the second tryptophan (W122) is less accessible to water than the first one (W124). Weaker W122^•+ solvation and electron-hole interaction with Re(dmp^•–) in CS2 makes W124^•+←W122 ET endergonic, shifting the CS1/CS2 equilibrium to CS1 where it undergoes unproductive recombination to the ground state (Scheme 1). We conclude that the uphill ET step is the main factor diminishing the Cu^II photoproduct yield (Scheme 1) (36). The situation is very different for PL/CRY where the terminal W₃^•+ (being stabilized with respect to W₂^•+) is produced faster than environmental water relaxation around the W₂^•+ intermediate.

The solvation gradient along a hopping pathway is the principal factor driving charge separation downhill while increasing water exposure enhances site-energy fluctuations, thereby increasing the probability of electronic-state crossings. Both these features are optimized in PL/CRY to achieve (ultra)fast high-yield charge separation. On the other hand, restricted W122 solvation in Re126WW diminishes its performance as a “Cu^I photo-oxidase.” Increasing the photoproduct yield would require enhancing water access to W122 by modifying the neighboring L120A119S118 α-helix or introducing a negatively charged residue to decrease the electrostatic potential at W122. We also expect enzyme protective pathways (25, 27, 81) to consist of progressively more solvated tryptophans and tyrosines that are more strongly electronically coupled to each other (73) than to the active site. This differential coupling will ensure efficient charge transport toward the enzyme surface without affecting enzymatic function.

In contrast to tryptophan chains, long-range hopping in multiheme proteins (28, 29) appears to be nonadiabatic, controlled by a delicate balance between driving forces and electronic couplings (30, 31). Cytochrome c cofactors are not directly water-exposed, and their formal potentials appear to be controlled by protonations of propionate side chains (82). Although there is no uniform downhill energy gradient along the cytochrome c sequences, endergonic ET steps are still fast, owing to increased electronic couplings. Compared to Re-azurins, heme units are coupled more weakly, |H_ab| < 8 meV, even when positioned at similar distances (30, 31).

Our simulations suggest that environmental effects on kinetics, thermodynamics, and charge-separation yields of hole hopping through tryptophan chains could differ in solutions or in viscous cell interiors or membranes. We expect that hopping will be disfavored in slowly relaxing environments, such as glycerol or trehalose solutions, provided that other factors stay constant. Solvent access emerges as a factor to consider when designing protein-based photocatalysts or bioelectronics. In the very interesting cases of electronic conductance in solvent-free protein films (83–87), delocalized electron transport (rather than hopping) is a possible mechanism.

Our work demonstrates that TDDFT-based multiscale QM/MM molecular dynamics simulations of the temporal evolution of low-lying excited-state manifolds can account for photoinduced ET processes, at least in well-coupled donor–acceptor assemblies in which individual redox states can be treated as electronic excited states of a single reference ground state. We suggest that this computational strategy could be useful for analyses of photoinduced charge separation in other large molecular systems, especially for elucidating molecular aspects of the reaction coordinate and the dependence of protein-mediated coupling on structure and structural fluctuations.

Methods

A detailed description of computational procedures is provided in SI Appendix, section S13. MD simulations of a series of low-lying triplet excited states of Re124W and Re126WW were performed at the QM/MM level in the Terachem 1.9 (88, 89)–Amber 14 (90) framework. The QM part of MD simulations utilized the UKS approach to describe the lowest triplet state and time-dependent DFT (TDDFT) for triplet excited-state manifolds, using the PBE0 functional (91, 92) with a D3 dispersion correction (93). Test calculations with a long range-corrected functional CAM-B3LYP (94) led to unrealistically large CT-CS energy separations at standard *Re geometries.

In calculating TDDFT/MM/MD, BO dynamics were run on the lowest adiabatic triplet state, and energies were referenced to the Re124W or Re126WW singlet ground state. This is a proper reference in the region before the *Re/CS1 crossing, but not afterward, where TDDFT energies dropped unrealistically. Nevertheless, TDDFT/MM/MD charge trajectories were not affected (SI Appendix, sections S6 and S13).

The *Re–CS1 couplings were calculated by an FCD method (58) at individual points of TDDFT/MM/MD trajectories in Qchem 5.2 software (95) using the PBE0 functional. Test calculations with long range-corrected functionals gave comparable or slightly higher |H_ab| values (SI Appendix, Table S3 and accompanying text). To calculate CS1–CS2 couplings on the B-3 trajectory, we recalculated the adiabatic energies of the lowest CS1 and CS2 states referenced to CS1.

Unique sets of MM parameters were derived for the ground state and lowest-triplet state of the Re chromophore in a solvated-protein environment, based on atomic charges and equilibrium bond lengths that were calculated separately (QM) for optimized structures of [Re^I(im)(CO)₃(dmp)]⁺ in its ground and lowest triplet state, respectively. Truhlar’s CM5 population analysis (96) was used to determine atomic charges instead of the standard restrained electrostatic potential procedure (97) that led to an unrealistic (overpolarized) charge distribution at the Re chromophore. Snapshots from *Re excited-state MM/MD trajectories provided initial positions and velocities for subsequent UKS/MM/MD simulations that, in turn, provided initial positions and velocities to calculate final TDDFT/MM/MD trajectories. Essentially, going from MM to UKS enabled ³CT/³IL fluctuations of *Re electronic structure and, hence, charge fluctuations. The solvent responded, and its fluctuations made *Re/CS1 crossings possible, possibly aided by high-frequency intramolecular vibrations. [SI Appendix, Fig. S35 shows g(r) shifting toward W124 in Re126WW on going from MM to UKS and then to TDDFT/MM/MD. A possible involvement of intramolecular vibrations is discussed in SI Appendix, section S12.] The CS1/CS2 crossing was examined on the trajectory B-3 without preceding MM and UKS steps. Nevertheless, some stabilization of the CS1 geometry occurred on B-3 during the 574 fs following *Re/CS1 crossing.

Our methodology inevitably involved approximations as needed to perform calculations in realistic times. Although BO dynamics could limit the description of the state-crossing event (43), we were able qualitatively to describe the system on approach to the crossing region. Further, our simulations did not involve polarization of the surroundings, and constant atomic charges were used.

Data Availability

All study data are included in the article and/or SI Appendix.